A new firefly algorithm-based superpixel clustering method for vehicle segmentation.

The vehicle segmentation in the images of a crowded and unstructured road traffic, having inconsistent driving patterns and vivid attributes like colour, shapes, and size, is a complex task. For the same, this paper presents a new firefly algorithm-based superpixel clustering method for vehicle segmentation. The proposed method introduces a modified firefly algorithm by incorporating the best solution for enhancing the exploitation behaviour and solution precision. The modified firefly algorithm is further used to obtain the optimal superpixel clusters. The modified firefly algorithm is compared against state-of-the-art meta-heuristic algorithms on IEEE CEC 2015 benchmark problems in terms of mean fitness value, Wilcoxon rank-sum test, convergence behaviour, and box plot. The proposed meta-heuristic algorithm performed superior on more than 80% of the considered benchmark problems. Moreover, the modified firefly algorithm is statistically better on more than 92% of the total problems during Wilcoxon test. Further, the proposed segmentation method is analysed on a traffic dataset to segment the auto-rickshaw. The performance of the proposed method has been compared with kmeans-based superpixel clustering method. The proposed method shows the highest mean value of 0.6242 for Dice coefficient. Both qualitative and quantitative results affirm the efficacy of the proposed method.

Introduction

All over the world, road accident is one of the fatal causes of death and takes 1.5 million (approx.) lives every year. The primary reason behind such a huge count is the distracted driving behaviour by humans (Dis 2021). To minimize the human control in driving, there has been a tremendous interest in the development of autonomous driving vehicles. Autonomous driving has great potential and advantages in controlling pollution, space utilization, traffic congestion, rule violation, and road accidents. Over a decade, researchers have worked upon various pilot projects to achieve better perception of the driving environment. One of the key steps in understanding the environment is the acute segmentation of surrounding vehicles. However, the predicament of an accurate and reliable vehicle segmentation is still a challenging task, especially in an unstructured driving environment. The main factors that effect segmentation accuracy in an unstructured scenario are non-lane driving, overloaded vehicles, road animals, occlusion, and missing lane trajectories. Additionally, the vehicle segmentation becomes trivial as vehicles do not follow a uniform design patterns. For illustration, Fig. 1 shows four representative images of auto-rickshaws that are taken from a publicly available dataset, termed as auto-rickshaw detection dataset (Aut 2021). To mitigate the above-mentioned complexities, this paper presents a new method by clustering the superpixels to segment the vehicles in an unstructured environment.

Fig. 1

Representative images of unstructured driving environment

Superpixels are the perceptual clustering of non-overlapping pixels with similar attributes. Generally, they are irregular-shaped but mean image regions which are formed by over-segmentation. Its advantages are in simplifying the image complexity and result in reduced processing time. Therefore, superpixels are used to extract mid-level features from an image in vivid computer-vision applications. Some of the common computer-vision applications are body model estimation, object localization, depth estimation, skeletonization, and image segmentation (Ibrahim and El-kenawy 2020). For image segmentation, deep learning methods have shown impressive performance. In general, deep learning-based models can be categorized into fully convolutional networks, encoder–decoder-based, recurrent neural network based(RNN), R-CNN-based, attention-based, deepLab family, and dilated convolutional-based (Long et al. 2015; Minaee et al. 2021). Long et al. (2015) proposed a fully convolutional network based on AlexNet, VGGNet, and GoogleNet for the purpose of pixel-wise prediction. However, the model is limited to only 2D images and is slow in real-time environment. To overcome the limitation of FCN, Liu et al. (2015) proposed ParseNet, which replaces the convolutional layers with the described module for the purpose of segmentation. Ronneberger et al. (2015) proposed the U-Net for image segmentation of biomedical datasets. Less number of annotated images can be trained and tested effectively using data augmentation. The network consists of two phases, namely contraction and expansion. The contraction phase captures the context information from the images while symmetric expansion path results in precise localization. Milletari et al. (2016) proposed V-Net based on FCN for 3D-image segmentation. Chen et al. (2014) proposed DeepLabV1 based on VGGNet and used atrous convolution and fully connected conditional random field, resulting in larger feature map. Furthermore, DeepLabV2 (Chen et al. 2017) is based on ResNet (Ismail Fawaz et al. 2019) as well as VGGNet (Simonyan and Zisserman 2014) and uses an additional atrous called as atrous spatial pyramid pooling (ASPP) making it more accurate than DeepLabV1. Despite the success of deep learning-based models for image segmentation, it has been witnessed in the literature that deep learning models face multiple challenges like gradient vanishing problem and high computational cost, and require highly challenging computation environment and memory. Moreover, the success of such models demands training over huge dataset with large number of annotated ground truths, which may not be readily available, especially in an unstructured driving environment.

Generally, the abundant availability of non-labelled data motivates the researchers to explore unsupervised learning approaches like clustering. Recently, Fouad et al. (2017) applied clustering with superpixels to perform the tissue segmentation from the oropharyngeal cancer images. Additionally, literature has witnessed that clustering is widely used as an exploratory tool due to its ability to identify hidden patterns (or structures) (Mittal and Saraswat 2018a). One of the common and popular clustering methods is Kmeans (Mittal et al. 2021c). It is a centroid-based method, which performs clustering of unlabelled data in non-overlapping and homogeneous clusters by using certain property measure such as separation or compactness of the clusters. This method has shown a number of advantages. First and foremost is the simplicity and guaranteed convergence of the Kmeans method. Second, it can be generalized over clusters with vivid size and shape. Further, it is adaptive in nature to new examples and can handle large data efficiently. However, it produces distinct clustering results with different parameter settings on same dataset (Mittal et al. 2021b). To overcome such limitation, meta-heuristic algorithms are widely employed in clustering (Mittal and Saraswat 2019b).

Meta-heuristic algorithms are the mathematical models of optimization based on various natural phenomena (Mittal and Saraswat 2018b). Some of the popular meta-heuristic algorithms are differential evolution (DE), genetic algorithm (GA), cuckoo search (CS), particle swarm optimization (PSO), and gravitational search algorithm (GSA) (Mittal et al. 2021a). In the literature, many meta-heuristic algorithms have been used for clustering (Kumar and Singh 2018). Gong et al. (2020) proposed an improved multi-level image segmentation method that integrates PSO with maximum entropy algorithm to speed up the segmentation process. Further, Sharma et al. (2020) proposed an entropy-based multi-level thresholding by employing firefly algorithm in order to find the optimal threshold. On the contrary, Yang et al. (2021) employed bat algorithm with Otsu and Kapur’s entropy as fitness functions for identifying optimal segmentation thresholds. Mittal et al. (2021b) presented improved gravitational search algorithm for generating optimal clusters to classify CT-scan images for COVID-19 detection. Vishnoi et al. (2021) proposed roulette wheel selection whale optimization to perform optimal clustering for segmentation of nuclei in histopathological images. Likewise, Sharma and Sharma (2021) performed optimal clustering of nuclei segmentation by employing grey wolf optimizer with multiple objectives. Kumar and Singh (2019) proposed a chaotic teaching learning-based optimization algorithm to address the clustering problems. Same authors presented an improved cat swarm optimization algorithm to efficiently cluster the UCI datasets (Kumar and Singh 2018). Further, Chinta (2019) combined traditional clustering methods with meta-heuristic algorithms like bat algorithm, cuckoo search algorithm, and krill herd algorithm for enhancing the convergence rate and stability of the outputs. From the literature, it has been observed that firefly algorithm (FA) (Yang 2009), one of the popular meta-heuristic algorithms, shows quite effective results on multimodal problems, especially on clustering applications (Xue 2020). Moreover, FA enhances the convergence of initial random solutions towards the optimal solution effectively (Wu et al. 2020). Therefore, this paper presents a new clustering-based image segmentation method to optimally cluster the superpixels by using the advantages of FA.

Firefly algorithm, proposed by Xin-She Yang (2009), is a popular meta-heuristic algorithm that mimics the social behaviour of fireflies. This algorithm is based on the flashing behaviour of the fireflies. Basically, FA formulates the mathematical model on three characteristics of fireflies: (i) Fireflies are attracted towards each other irrespective of their sex, (ii) the attraction among fireflies is inversely propositional to the distance among them, and (iii) the level of brightness defines the level of attraction, i.e. fireflies with less brightness will be attracted to more brighter fireflies. In case of equal brightness, fireflies will move randomly. In the literature, FA has shown superior performance than a number of existing meta-heuristic algorithms and has been employed to solve a number of real-world optimization problems (Fister et al. 2013). Sánchez et al. (2017) optimized modular granular neural network with FA to perform facial recognition. Jain and Katarya (2019) performed opinion mining with FA on social networking data. Further, Wang et al. (2018) employed FA for big data optimization. Langari et al. (2020) applied FA to search optimal fuzzy clusters to minimizing the information loss on anonymized database. Similarly, Hrosik et al. (2019) introduced FA with Kmeans for brain segmentation. A comprehensive survey on the applications of FA can be found in Kumar and Kumar (2021). Yang and He (2013) identified two main reasons for the good performance of FA, i.e. subdivision of search space intelligently and ability of handling multimodal problems. However, it has been observed that FA suffers from a number of demerits such as poor exploitation ability, slow convergence rate, and low solution precision. To mitigate the same, this paper proposes a modified FA (MFA). Moreover, the proposed MFA is employed to optimally segment the vehicles from the images.

The overall contribution of the paper has twofold: (i) a modified firefly algorithm (MFA) has been proposed and (ii) a new modified firefly algorithm-based superpixel clustering (MFA-SC) method has been introduced to segment the vehicles from images. To validate the proposed MFA, seven recent meta-heuristic algorithms, namely firefly algorithm (SFA), improved particle swarm optimization (IPSO), enhanced differential evolution (EDE), improved artificial bee colony (IABC), improved biogeography-based optimization (IBBO), enhanced grey-wolf optimization (EGWO), and improved whale optimization algorithm (IWOA), have been considered. Experimental analysis has been conducted on CEC2015 benchmark functions in terms of mean fitness values, Wilcoxon rank-sum test, convergence graph, and box plot. Moreover, the proposed clustering method (MFA-SC) has been evaluated on a publicly available dataset, namely auto-rickshaw detection dataset (Aut 2021). To compare the performance, two clustering methods, namely firefly algorithm-based superpixel clustering (FA-SC) and kmeans-based superpixel clustering (Kmeans-SC), have been considered and equated in terms of qualitative and quantitative parameters. Moreover, the computational time of the proposed method has been presented.

The rest of the paper is organized as follows: Section 2 briefs the superpixel generation method and firefly algorithm. The proposed method is detailed in Sect. 3. Section 4 discusses the experimental analysis followed by the conclusion along with future directions in Sect. 5.

Preliminaries

The proposed firefly algorithm-based superpixel clustering (MFA-SC) method uses the simple linear iterative clustering method to generate the superpixels and firefly algorithm for optimal clustering. The following section briefly presents both the methods.

Simple linear iterative clustering method

Simple linear iterative clustering (SLIC) method (Achanta et al. 2012) is one of the popular methods for superpixel generation as it needs only the number of superpixels (P) as parameter. There are two phases in SLIC method, namely initialization and local clustering. In the first phase, S superpixel centroids are initialized at an interval for (N) number of pixels. During local clustering, distance of each pth superpixel centroid is calculated from the ith image pixel in image region according to Eq. (1).where m is a constant, while and correspond to the Euclidean distance between ith and pth pixels in two different colour space, i.e. CIELab (l, a, b) and spatial (x, y), which are depicted in Eqs. (2) and (3), respectively.Equation (1) assigns each image pixel with the closest superpixel centroid. Further, each superpixel centroid is updated by averaging the assigned pixels. Later, the remaining ones are associated with the closest superpixel centroids.

Firefly algorithm

Firefly algorithm (FA) (Yang 2009) mimics the social behaviour of fireflies to obtain optimal solution. It works on the flashing behaviour of fireflies. The mathematical modelling of fireflies is based on the following three rules.As level of attractiveness is inversely propositional to distance, the attraction level () at distance r can be defined as Eq. (4).where is a light absorption coefficient and corresponds to the level of attractiveness at . In Eq. (4), r is the Cartesian distance between two fireflies.

Fireflies are attracted towards each other irrespective of their sex.

The attraction among fireflies is inversely propositional to the distance among them.

The level of brightness defines the level of attraction, i.e. fireflies with less brightness will be attracted to more brighter fireflies. In case of equal brightness, fireflies will move randomly. Moreover, the level of brightness depends upon the landscape of the objective function.

Further, the position () of ith firefly at time is updated by moving it to a more attractive jth firefly, which is formulated in Eq. (5).where is a randomized parameter in [0,1], while is a random vector. Algorithm 1 describes the pseudo-code for the firefly algorithm.

Proposed method

This paper presents a new modified firefly algorithm-based superpixel clustering (MFA-SC) to perform the image segmentation. Specifically, the proposed method is used to segment the vehicles from an image. Figure 2 illustrates the block diagram of the proposed method. In the proposed method, the colour image is processed through the SLIC method. This preprocessing results in generating superpixels, which are irregular-shaped and non-overlapping image regions with similar attributes. This reduces the processing time of the image. Next, the set of image portions are further optimally clustered by employing the proposed MFA. To generate ‘q’ optimal clusters, MFA initializes its population with random values. Each individual of MFA depicts ‘q’ cluster centroids with ‘d’ dimensions, where ‘d’ corresponds to the number of considered attributes for superpixels. Next, the fitness of each individual is evaluated according to the considered objective function. In the proposed method, the objective function is equated as the Euclidean distance between cluster centroid and corresponding superpixel whose mathematical formulation is depicted in Eq. (6).where q and N correspond to the number of cluster centroids and number of superpixel centroids, respectively. The and represent the ith cluster centroid and sth superpixel centroid, respectively.

Fig. 2

Block diagram of the proposed method

Further, each individual is updated according to the proposed MFA until the stopping criteria. A detailed discussion of the MFA is presented in Sect. 3.1. Finally, the optimal cluster centroids, returned by MFA at the stopping criteria, operate on the considered image to segment the vehicle from the background. The pseudo-code of the proposed method is presented in Algorithm 2.

Modified firefly algorithm

In firefly algorithm, the position of a firefly is updated according to the distance between two fireflies. However, FA does not consider the best solution in position update equation, which results in attaining poor solution precision sometimes. To improve the same, a new modified firefly algorithm is proposed in this paper. In the proposed modified firefly algorithm (MFA), the updated position of a firefly is modified by including the position of the best firefly. This incorporation considers the position difference between the current best and considered firefly. This benefits in moving the fireflies towards the best solution. Further, this component is multiplied with a random value, which varies the movement of the MFA. Overall, this enhances the exploitation behaviour of the MFA towards the best solution, which results in attaining better solution precision. The formulation of the modified position update equation for firefly at time is depicted in Eq. (7).where corresponds to the position of the best firefly at time (t). This enhances the exploitation behaviour of the fireflies towards the best solution, which results in attaining better solution precision. The pseudo-code of the proposed MFA is detailed in Algorithm 3.

The time complexity of the proposed method (MFA-SC) is based upon three factors, namely SLIC method, objective function, and modified firefly algorithm (MFA). SLIC method has the time complexity of O(N) for N number of superpixels (Mittal and Saraswat 2019a). The considered objective function computes Euclidean distances between cluster centroid and superpixel centroid. Thus, the time complexity of the objective function is , where q is the number of cluster centroids. Lastly, MFA has same time complexity as FA, i.e. (Yang and He 2013), where p and t correspond to population size and number of maximum iterations in FA. Thus, MFA-SC method has the total time complexity of (). However, the number of superpixels is generally more than p and t. Therefore, the time complexity of MFA-SC is equal to .

Experimental results

This paper explores the performance of the proposed vehicle segmentation method in two sections. Section 4.1 studies the experimental validation of the proposed modified firefly algorithm (MFA) on IEEE Congress on Evolutionary Computation 2015 (CEC2015) (Liang et al. 2014). In Sect. 4.2, the proposed method (MFA-SC) is analysed on a publicly available dataset, termed as auto-rickshaw detection dataset (Aut 2021). All experiments are simulated on MATLAB2016a on a system of 3.35 GHz with Intel i5 processor and 16GB RAM.

Performance analysis of MFA

To evaluate the performance of the proposed MFA, a set of 15 real-parameter single-objective optimization problems of IEEE CEC2015 (–) (Liang et al. 2014) is considered, which is depicted in Fig. 3 along with the respective optimal value. This set includes unimodal, multimodal, hybrid, and composite problems to validate the robustness of MFA. The efficiency of the MFA is compared against firefly algorithm (FA) (Yang 2009) and six recent meta-heuristic algorithms, namely improved particle swarm optimization (IPSO) (Zhang and Lim 2020), enhanced differential evolution (EDE) (Chacón Castillo and Segura 2020), improved artificial bee colony (IABC) (Ewees et al. 2020), improved biogeography-based optimization (IBBO) (Zhang et al. 2019), enhanced grey wolf optimization (EGWO) (Cai et al. 2019), and improved whale optimization algorithm (IWOA) (Qiao et al. 2020). Table 1 defines the parameter settings of the considered algorithms by referring the corresponding literature. For minimum interference, each algorithm is executed for 30 runs over three dimensions, i.e. 30, 50, and 90.

Fig. 3

Description of considered real-parameter single-objective optimization problems of IEEE CEC2015 (Liang et al. 2014)

Table 1

Parameter settings of the considered meta-heuristic algorithms

Parameter	Values
Population size	50
Maximum iterations	1000
Population size	50
No. of runs	30
Considered dimensions	30, 50, 90
IPSO
Velocity	0.6
Inertia weight	0.8
EDE
Crossover rate	[0.2–0.9]
IABC
Modification rate	0.8
IBBO
Immigration rate	1
EGWO
Crossover probability	0.2
IWOA
Weight	[0.5–0.8]
Jumping probability	0.1
FA and MFA
β_0	0.2
γ	1

In Table 2, the mean fitness values reported by the considered algorithms are presented on the IEEE CEC2015 benchmark problems (–) over the considered dimensions. The bold text in the table depicts the best value among the compared algorithms. On 30 and 50 dimensions, the proposed MFA outperforms the compared algorithms on all benchmark problems except , , , and . However, MFA produces competitive results on and for both dimensions. This clearly demonstrates that modification in FA results in attaining better precision. Moreover, MFA reports superior values on all benchmark problems, except and , when executed on 90 dimensions. This accounts for more than 80% of the considered problems. On , MFA has generated comparative results. Moreover, MFA is able to obtain comparable mean fitness values on remaining problems. Therefore, it can be stated that MFA exhibits better performance on higher dimensions. Moreover, it can be envisioned from Table 2 that MFA can maintain better balance between exploration and exploitation over problems of different complexities.

Table 2

Mean fitness value reported by the considered algorithms over the IEEE CEC2015

Dims.	Algo.	C_1	C_2	C_3	C_4	C_5	C_6	C_7	C_8
30	IPSO	8.42E+06	2.01E+04	2.09E+01	7.12E+01	4.36E+03	9.52E+05	1.20E+01	2.56E+05
	EDE	5.22E+07	3.99E+05	2.08E+01	1.72E+02	6.02E+03	3.90E+06	1.44E+01	7.58E+05
	IABC	6.20E+08	2.70E+06	2.10E+01	2.41E+02	7.96E+03	1.61E+07	1.91E+01	6.38E+02
	IBBO	6.74E+07	1.91E+09	2.00E+01	2.37E+02	4.21E+03	2.17E+06	6.87E+01	1.08E+05
	EGWO	8.07E+06	1.57E+03	2.01E+01	1.50E+02	3.75E+03	2.33E+05	1.86E+01	7.81E+04
	IWOA	3.80E+07	5.58E+08	2.01E+01	2.49E+02	4.28E+03	1.37E+06	1.91E+01	6.46E+05
	FA	9.51E+07	1.32E+10	2.00E+01	4.58E+02	4.47E+03	1.06E+06	6.45E+01	1.56E+05
	MFA	9.85E+04	3.74E+03	2.09E+01	5.15E+01	2.87E+03	3.98E+04	4.65E+00	2.40E+04
50	IPSO	5.51E+07	7.27E+06	2.12E+01	1.74E+02	9.60E+03	4.35E+06	8.83E+01	3.55E+06
	EDE	4.44E+08	1.08E+07	2.11E+01	3.83E+02	1.23E+04	2.47E+07	6.13E+01	9.94E+06
	IABC	4.26E+09	1.43E+10	2.12E+01	5.75E+02	1.48E+04	1.26E+08	3.79E+01	3.92E+07
	IBBO	8.28E+08	3.40E+10	2.00E+01	4.26E+02	6.77E+03	1.12E+07	1.11E+02	5.20E+06
	EGWO	3.01E+07	7.66E+03	2.02E+01	3.28E+02	7.01E+03	2.50E+06	7.43E+01	2.33E+06
	IWOA	1.06E+08	4.20E+09	2.03E+01	5.51E+02	7.15E+03	2.84E+06	1.20E+02	2.84E+06
	FA	7.02E+08	6.10E+10	2.00E+01	8.50E+02	7.57E+03	9.73E+06	2.73E+02	2.99E+06
	MFA	8.38E+05	1.35E+04	2.11E+01	1.35E+02	5.02E+03	2.46E+05	3.81E+01	1.52E+05
90	IPSO	2.48E+08	1.59E+09	2.13E+01	7.15E+02	2.87E+04	4.14E+07	2.07E+02	1.96E+07
	EDE	3.15E+09	2.41E+08	2.13E+01	1.06E+03	3.05E+04	2.50E+08	1.77E+02	1.17E+08
	IABC	1.43E+10	4.38E+11	2.14E+01	2.21E+03	3.29E+04	1.58E+09	4.99E+02	5.44E+08
	IBBO	1.85E+09	1.79E+11	2.00E+01	9.51E+02	1.56E+04	3.71E+08	1.72E+03	4.13E+07
	EGWO	1.49E+08	8.28E+07	2.03E+01	8.61E+02	1.79E+04	1.27E+07	1.95E+02	8.79E+06
	IWOA	3.45E+08	1.62E+11	2.08E+01	1.54E+03	2.00E+04	2.12E+07	4.66E+02	1.05E+07
	FA	2.13E+09	2.54E+11	2.00E+01	1.81E+03	1.55E+04	1.52E+08	1.56E+03	2.84E+07
	MFA	6.50E+06	7.13E+03	2.13E+01	3.73E+02	1.27E+04	1.54E+06	1.28E+02	6.73E+05

Bold font: Best value

Further, a statistically test, Wilcoxon rank-sum test, is conducted to validate the performance of the MFA against considered algorithms. Table 3 tabulates the results of the test. Here, ‘’ means that MFA is significantly better than the compared algorithm, while ‘−’ symbolizes the reverse. On the contrary, ‘’ depicts that the compared algorithms are not significantly different. From Table 3, it can be observed that MFA obtains ‘’ on maximum number of problems when compared to EDE, IWOA, and FA for all the considered dimensions, which show its superiority over considered algorithms. Overall, MFA is statistically better on more than 92% of the total problems, which validates that MFA is significantly better and different than the considered algorithms.

Table 3

Results of the Wilcoxon rank-sum test of MFA when compared with other considered algorithms

Dims.	Funct.	IPSO	EDE	IABC	IBBO	EGWO	IWOA	FA
30	C_1	+	+	+	+	+	+	+
	C_2	+	+	+	+	=	+	+
	C_3	=	+	+	−	+	+	+
	C_4	+	+	+	+	+	+	+
	C_5	+	+	+	+	+	+	+
	C_6	+	+	+	+	+	+	+
	C_7	+	+	+	+	+	+	+
	C_8	+	+	+	+	+	+	+
	C_9	+	+	+	+	+	+	+
	C_10	+	+	+	+	+	+	+
	C_11	+	+	+	=	+	+	+
	C_12	+	+	+	+	+	+	+
	C_13	+	+	−	+	+	+	+
	C_14	+	+	−	+	+	+	+
	C_15	+	+	+	+	+	+	+
50	C_1	+	+	+	+	+	+	+
	C_2	+	+	+	+	=	+	+
	C_3	+	+	+	−	+	+	+
	C_4	+	+	+	+	+	+	+
	C_5	+	+	+	+	+	+	+
	C_6	+	+	+	+	+	+	+
	C_7	+	+	−	+	+	+	+
	C_8	+	+	+	+	+	+	+
	C_9	+	+	+	+	+	+	+
	C_10	+	+	+	+	+	+	+
	C_11	+	+	+	=	+	+	+
	C_12	+	+	=	+	+	+	+
	C_13	+	+	−	+	+	+	+
	C_14	=	+	−	+	+	+	+
	C_15	+	+	+	+	+	+	+
90	C_1	+	+	+	+	+	+	+
	C_2	+	+	+	+	+	+	+
	C_3	=	+	+	+	+	+	+
	C_4	+	+	+	+	+	+	+
	C_5	+	+	+	+	+	+	+
	C_6	+	+	+	+	+	+	+
	C_7	+	+	+	+	+	+	+
	C_8	+	+	+	+	+	+	+
	C_9	+	+	+	+	+	+	+
	C_10	+	+	+	+	+	+	+
	C_11	+	+	+	+	+	+	+
	C_12	+	+	=	+	+	+	+
	C_13	+	+	−	+	+	+	+
	C_14	+	+	+	+	+	+	+
	C_15	+	+	+	+	+	+	+

To study the searching behaviour, Fig. 4 plots the convergence trend of the considered algorithms on four representative problems, namely , , , and , belonging to unimodal, multimodal, composite, and hybrid category of IEEE CEC2015, respectively, when executed for 30 dimension. In the figure, x-axis depicts the total number of considered iterations, while y-axis presents the best fitness value in an iteration. It can be observed that MFA is obtaining better value while maintaining the balance between exploration and exploitation. The convergence trend for (Fig. 4b) is quite different due to the functional settings of the considered problem. As it is a multimodal problem, the algorithm is unable to show the smooth trend. However, the proposed MFA still achieves the optimal solution. From Fig. 4b, it can be observed that MFA moves slowly till 700 iteration. Afterwards, it converges abruptly and attains the optimal solution. These results suggest that MFA is a better algorithm in terms of search behaviour and solution precision.

Fig. 4

Convergence plots of the considered algorithms on four IEEE CEC2015 problems

Moreover, the variation in mean fitness values obtained by the considered algorithms over 30 runs on 30 dimension is analysed in the form of box plot. Figure 5 draws the box plots of considered algorithms for four representative problems, namely , , , and , where each problem belongs to different categories of IEEE CEC2015. It is clearly visible from the figure that the interquartile range and median value for MFA are comparatively low than the compared algorithms in every considered problem. Therefore, it can be claimed that MFA is more consistent in obtaining the optimal solutions. Further, the applicability of the proposed variant (MFA) is studied in the following section as a clustering method for segmenting the vehicles in an unstructured environment.

Fig. 5

Box-plot analysis of the considered algorithms on four IEEE CEC2015 problems

Performance analysis of proposed segmentation method

The efficiency of the proposed clustering method, modified firefly algorithm-based superpixel clustering (MFA-SC), is studied to segment the vehicles in an unstructured environment. In such scenario, vehicles, such as auto-rickshaws, make the segmentation task complex due to vivid attributes like colour, shapes, and size. Moreover, auto-rickshaws have inconsistent driving patterns. To illustrate such complexities of auto-rickshaws, IIIT-Hyderabad provided a public dataset termed as auto-rickshaw detection dataset (Aut 2021). This dataset consists of around 1000 images along with bounding-box annotations for each instance of auto-rickshaw. The bounding-box annotation is used to generate the segmentation ground truths. Further, each image is resized to size. Moreover, each image is preprocessed to 2000 superpixel, which are further clustered in 2 segments, one segment depicts the region of interest (RoI), i.e. auto-rickshaw, while another segment represents the image background. The segmentation performance of the proposed method (MFA-SC) is analysed in terms of qualitative and quantitative parameter, i.e. Dice coefficient (DC). The mathematical formulation of DC is defined in Eq. (8).where x and y are the segmented area, generated by the proposed method, and segmented area in ground-truth image, respectively. Higher value of DC shows the better segmentation. Furthermore, the obtained results are compared against two clustering methods, namely firefly algorithm-based superpixel clustering (FA-SC) and kmeans-based superpixel clustering (Kmeans-SC). The parameter settings of the considered methods are referred from Table 1.

Table 4 lists the DC values of the considered methods for ten randomly selected images. In the table, MFA-SC reports DC values of more than 0.94 on all the considered images. Specifically, MFA-SC attains maximum DC value of 0.9843 and minimum DC value of 0.9456. On the other side, FA-SC and Kmeans-SC achieved the maximum DC value of 0.9508 and 0.8767, while the minimum DC value reported by these methods is 0.8808 and 0.7293, respectively. Moreover, mean DC value over the entire dataset is highlighted in Table 4. It can be clearly seen that MFA-SC has outperformed the considered methods in segmentation. MFA-SC has reported the performance improvement of 4% and 48% approximately in comparison with FA-SC and Kmeans-SC, respectively. For the same, bar chart is plotted in Fig. 6 for easy visualization. As high DC value corresponds to better segmentation, it can be claimed that MFA-SC ranks first with mean value of 0.6242, while FA-SC and Kmeans-SC attain second and third ranks with mean values of 0.6062 and 0.4282, respectively. Further, Fig. 7 illustrates the variation of the obtained DC values by the considered methods over the entire dataset. It is observable that MFA-SC achieves higher median value comparatively. Moreover, the interquartile range of the proposed method is low. This suggests that MFA-SC reports comparatively better segmentation results over the entire dataset. To do qualitative analysis, Figs. 8 and 9 depict the segmentation results of the considered methods on eight sample images, wherein first column contains the original images, while second, third, and fourth columns present the results of the MFA-SC, FA-SC, and Kmeans-SC, respectively. It is envisaged that the auto-rickshaw is visually clear in all the segmented images of MFA-SC in comparison with other methods. Moreover, the proposed method is able to distinguish auto-rickshaws with different colours and environmental complexities efficiently. Therefore, experiments clearly affirm the superiority of the proposed method.

Table 4

Comparison of the DC values obtained by the considered methods

Image	MFA-SC	FA-SC	Kmeans-SC
Image 1	0.9600	0.8808	0.7635
Image 2	0.9456	0.9031	0.7301
Image 3	0.9843	0.9456	0.7673
Image 4	0.9455	0.9092	0.7652
Image 5	0.9469	0.9097	0.7415
Image 6	0.9683	0.9399	0.7391
Image 7	0.9465	0.9484	0.7631
Image 8	0.9841	0.9154	0.7293
Image 9	0.9600	0.9508	0.8767
Image 10	0.9508	0.9070	0.7579
Mean	0.6242	0.6062	0.4282

Fig. 6

Bar chart of mean DC values obtained by considered methods over the entire dataset

Fig. 7

Variation in DC value obtained by the considered methods over entire dataset

Fig. 8

Segmentation results by the considered methods over four representative images

Fig. 9

Segmentation results by the considered methods over four representative images

Furthermore, the computational time (in seconds) taken by the considered methods to perform the segmentation over the ten images is compared in Table 5. It can be seen that MFA-SC and FA-SC methods are computationally expensive than Kmeans-SC. However, segmentation accuracy is an important factor than computation time, and MFA-SC has shown superior efficiency than the compared methods. Thus, it can be concluded from experimental analysis that the proposed method produces better segmentation results and is an efficient alternative for segmentation.

Table 5

Comparison of computational time (in seconds) of the considered methods

Image	MFA-SC	FA-SC	Kmeans-SC
Image1	44.616	44.981	0.041
Image2	39.612	40.190	0.028
Image3	43.402	43.631	0.020
Image4	37.929	38.077	0.028
Image5	40.546	41.318	0.020
Image6	34.409	35.531	0.021
Image7	30.446	31.953	0.034
Image8	35.127	35.787	0.026
Image9	32.083	32.910	0.030
Image10	41.142	41.409	0.026

Conclusion

This paper proposes a new clustering method, modified firefly algorithm-based superpixel clustering (MFA-SC), for the segmentation of vehicles in an unstructured environment. In the proposed method, a new modified firefly algorithm (MFA) is employed to obtain optimal clusters. MFA modifies the position updation by incorporating the best solution, which enhances the exploitation behaviour and results in attaining better solution precision. The performance of the proposed variant is compared against seven meta-heuristic algorithms, namely firefly algorithm (FA), improved particle swarm optimization (IPSO), enhanced differential evolution (EDE), improved artificial bee colony (IABC), improved biogeography-based optimization (IBBO), enhanced grey wolf optimization (EGWO), and improved whale optimization algorithm (IWOA), on a set of 15 real-parameter single-objective optimization problems of IEEE CEC2015. The results of the considered algorithms are analysed in terms of mean fitness value, Wilcoxon rank-sum test, convergence behaviour, and box plot. Experimental results have demonstrated that MFA performed superior on more than 80% of the considered problems. Moreover, MFA is statistically better on more than 92% of the total problems during Wilcoxon test. Consequently, the analysis of the proposed method (MFA-SC) on a public dataset, known as auto-rickshaw detection dataset, has been conducted in terms of qualitative and quantitative parameters, i.e. Dice coefficient (DC). The proposed method (MFA-SC) has achieved the highest mean value for Dice coefficient (DC), i.e. 0.6242, while FA-SC and Kmeans-SC reported the DC value of 0.6062 and 0.4282, respectively. Both visual and numerical results evident that the proposed method is efficient in comparison with firefly algorithm-based superpixel clustering and kmeans-based superpixel clustering. Moreover, experiments have elicited that the proposed method has efficaciously segmented the auto-rickshaws in reasonable time limit.

In future, the proposed method can be extended to work in real-time environments like internet of things. Further, big-data technologies like, Hadoop or PySpark, can be used to handle the large image dataset efficiently. Moreover, the concept of fuzzification can be incorporated into the proposed method for analysing images with overlapping or complex backgrounds. Lastly, different objective functions, such as structural similarity index or boundary displacement error, can be explored for better performance of the proposed method.